The boundary between compact and noncompact complete Riemann manifolds D. HolcmanCharles Pugh 53C1553C20Riemannian geometryasymptotic manifoldspositive Ricci curvatureextension of Myer's theorem In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum, then the manifold is compact and its diameter is bounded in terms of the infimum. Subsequently the curvature hypothesis has been weakened, and in this paper we weaken it further in an attempt to find the ultimate, sharp result. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2860 10.1512/iumj.2007.56.2860 en Indiana Univ. Math. J. 56 (2007) 437 - 458 state-of-the-art mathematics http://iumj.org/access/